\newproblem{lay:2_8_28}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.8.28}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Nov. 11th, 2013} \\}{}

  % Problem statement
	Construct a $3\times 3$ matrix $A$ and a vector $\mathbf{b}$ such that $\mathbf{b}$ is not in $\mathrm{Col}\{A\}$.
}{
  % Solution
	Consider the matrix $A=\begin{pmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{pmatrix}$ and $\mathbf{b}=\begin{pmatrix}0 \\ 0 \\ 1\end{pmatrix}$. Obviously,
	$\mathbf{b} \notin \mathrm{Col}\{A\}$ because there is no way that we can combine the columns of the matrix $A$ to obtain a 1 in the third component.
}
\useproblem{lay:2_8_28}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
